Thanks in advance for any critique you can give. I'm not sure how readable or interesting this is, so I'd greatly appreciate feedback on, y'know, if it was worth reading. Like I said in the summary, it's been through a couple cycles in chat, so hopefully it's at least alright. I know immortality is kinda a gimmick, but I think I've got a novel approach.

Give the author an action to follow! Just saying "I like this a lot" / "I don't like this" is also too vague. What specific parts were good and can be kept after edits? What parts are weaker and can be trimmed?

The feedback you've given here does not help the author improve the piece, nor does it give them any new knowledge to act on should others react more negatively than you did.

SCP-XXXX does not age past 31 years old, supposedly the age it became anomalous.

"Supposedly" isn't particularly clinical. I suggest that you instead identify this information as having been provided by SCP-XXXX. This also helps with the specificity of age. While it's not too hard to tell a one year old from a two year old, telling a 31 year old from a 32 year old is stretching belief somewhat.

A cemetery worker in Anzio, Italy called the police after hearing a thumping noise in an unknown war grave.

I think I mentioned it in chat - this sentence is to storytelling. It might be better to go with something along the lines of "Police were alerted to SCP-XXXX after a cemetery worker in Anzio, Italy reported hearing a thumping noise in an unidentified war grave", or something along those lines. Notice that I've changed the tense from "this is happening right now" to "this is what happened"

Local officers opened the grave and discovered a near-severed head striking the side of the casket, while its body was inanimate.

Partially decapitated head is a bit more clinical. On a personal note, it also provides me with a more visceral image.

The first collapsible says Interview XXXX-C before being opened, and Interview XXXX-A after being opened

SCP-XXXX had claimed worsening nightmares in recent weeks and refused to participate in a combat test until forced.

I have a couple of problems with this sentence. First, I'd stay away from saying "claimed" - it makes it sound like the Foundation arbitrarily doesn't believe this statement. "Reported" might be a better choice.
I also think that implying that the Foundation forced SCP-XXXX to participate in a combat test might be pushing the line a bit, but that may be personal preference.

She decided to try exposure treatment.

Exposure therapy.

When Richardson exited the coffin, the guard advised her to end the treatment there and she refused.

A well trained guard would know better than to interfere with Foundation experiments. Saying that "she refused" also implies that this guard knows better than a trained researcher, and, to me at least, feels like male chauvinism in the reporting of this incident.

SCP-XXXX: I asked to speak to the doctor, not you.

Dr. Reynolds: You aren't allowed to see her. Too dangerous.

Why is it too dangerous for Dr. Richardson, but not for Dr. Reynolds? I'd suggest either ditching Reynolds and continuing with Richardson, or changing the reason for her absence to being taking time off to heal.

You call them the Immortals.

Well, that came left of field. I wasn't aware that the Foundation had a term for SCP-XXXX's men. This needs to be established, or removed.

I see that you've changed him from a happy-go-lucky immortal guy to someone with serious issues, and a backstory as well. This is a much more interesting SCP than the draft I read in chat, so well done making such a big change.